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CGP EDU Academic Team
Published on: August 12, 2026
Given f(x) = x 2 e 2(x – 1) , 0 ≤ x ≤ 1= a sgn (x + 1) cos (2x – 2) + b x 2 , 1 < x ≤ 2,
f(x) is differentiable at x = 1 provided
Text Solution
Verified by ExpertsThe correct answer is:
A
f(1 – ) = 1 = f(1) and f(1 + ) = a + b
For continuity at x = 1, a + b =1 ……(i)
In 0 < x < 1, f '(x) = 2xe 2(x – 1) + 2x 2 e 2(x – 1) ∴ f '(1
– ) = 4
In 0 < x < 2, f ' (x) = – 2a sin (2x – 2) + 2bx
∴ f '(1 + ) = 2b
For differentiability at x = 1, 2b = 4. This with (1) gives the values a = – 1, b = 2.
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